The classic Washington political drama—will he go or will he stay?—is now swirling around Eric Shinseki, the secretary of the Department of Veterans Affairs. It could be weeks or months before we know the answer.

Good, his critics might retort. He may end up waiting as long to learn his fate as some of those veterans have waited for appointments with one of his 300,000 employees.

The critics have a point. Despite the high grades the VA gets for tending to the ailments of the nation’s vets, it has always had problems seeing them quickly enough when they need help—or when they are seeking disability benefits. Such wait-list problems have persisted for years, even as the VA’s budget has tripled, to $150 billion annually, since 9/11.

The VA debate over fudged appointment waiting times—possibly leading to vet deaths—reached a critical point over the weekend. There was a call from the Washington Post‘s Dana Milbank on Sunday for Shinseki to go (“His maddeningly passive response to the scandal suggests that the best way Shinseki can serve now is to step aside.”) That was echoed by the independent Army Times, which said in an editorial that “allowing the status quo at VA to remain intact is unacceptable.”

Even Duffel Blog, a military version of the Onion, got into the act. “VA: Please Hold,” it headlined a post. “You Should Hang Up And Just Watch Cat Videos Instead.” Once a political predicament has curdled into farce, the sharks begin circling. The scent of blood in the water spiked Friday when Shinseki accepted the premature retirement of Robert Petzel, the VA’s undersecretary for health care.

But Shinseki has his defenders. “The President is madder than hell” over the mess at the VA, White House chief of staff Dennis McDonough said Sunday on CBS’s Face the Nation. Shinseki, he added, “will continue to work these issues until they’re fixed.” Defense Secretary Chuck Hagel and Army General Martin Dempsey, chairman of the Joint Chiefs of Staff, have endorsed Shinseki’s continuing tenure. So has Max Cleland, a triple amputee from the Vietnam war, who ran the VA under Jimmy Carter.

Dr. Sam Foote, a key VA whistleblower, said Sunday that Shinseki should remain on the job. “I think our best bet at this point is to keep the secretary onboard,” he told Fox News, “but I think the President needs to keep him on a pretty short leash.”

Following two of the nation’s longest wars, the VA has become a political tool, because veterans are a potent political force. Like politicians embracing the status quo on Social Security, there is scant downside to nodding in agreement with whatever veterans say. There was a lot of heat at last week’s Senate Veterans Affairs Committee hearing where Shinseki and Petzel testified, but little illumination, from them or anyone else. It’s worth noting that beyond the American Legion, which has called for Shinseki’s replacement, most veterans groups support, or haven’t take a position on, Shinseki’s future.

But the anger among some veterans is palpable. Shinseki, in his low monotone, seems unperturbed by the problems happening on his watch. Such stoicism—probably a side effect of his 38 years in uniform—doesn’t play well in today’s political arena. It seems as if you’re not breathing fire, you don’t care.

Army Times, in its editorial calling for Shinseki’s ouster, noted that he’s not a chest-thumping, bellowing commander. “Going back to his four-star days as Army chief of staff, Shinseki has long been recognized as a behind-the-scenes leader, one who uses his influence outside the public eye,” its editorial said. “Unfortunately, that’s simply the wrong style for what VA needs now.”

Apparently style-over-substance is now a job requirement at the VA. It’s worth recalling that it was more than a decade ago that Shinseki, then the Army chief, told another Senate panel—the armed services committee—that it would likely take “several hundred thousand soldiers” to pacify Iraq post-invasion. His best military assessment angered Defense Secretary Donald Rumsfeld and his deputy, Paul Wolfowitz, who thought far fewer troops would be needed. Shinseki’s public pronouncement left him a lame-duck member of the Joint Chiefs as the nation waged two wars, even as history ended up siding with him.